C.M. Caves, R. Schack, "Unpredictability, information, and chaos", LANL chao-dyn/9705013. Home/Search Document Not in Database Summary Related Articles Check |
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Lyapunov Exponents, Stability and Information - Hugo Touchette Mechanical (Correct)
....connection between the two measures is more subtle than that implied by this interpretation. For instance, K is a purely dynamical quantity whereas S refers usually to static or equilibrium systems. Here, instead of going through the formal dynamical definition of this quantity [4] we follow [1, 15] and assume implicitely the similarity between S and K to define the latter quantity. 3.1. Kolmogorov entropy To begin, let us focus our attention on the trajectory picture of dynamical systems. Consider the trajectory x (t) of a D dimensional dynamical system and suppose that we apply a uniform ....
....K(ae) lim l 0 lim N 1 1 N N Gamma1 X n=0 [K(n 1) Gamma K(n) 43a) Gamma lim l 0 lim N 1 1 N X i 0 ; i N Gamma1 p(i 0 ; i N Gamma1 ) ln p(i 0 ; i N Gamma1 ) 43b) 10 F C i j Figure 4: Evolution of a density in a coarse grained phase space. From [1]) In this expression, the dependence on ae has been explicitely written to remind the reader that K is an ergodic quantity is the sense of x2. Also, the limit l 0 is there to make K independent of the partition F . From the density picture, a similar expression may be obtained as follows [1] ....
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C.M. Caves, R. Schack, "Unpredictability, information, and chaos", LANL chao-dyn/9705013.
Quantum Information Theory - Barnum, III (1998) (Correct)
....useful in quantum cryptography. And there is a myriad of other motivations for interest in quantum information theory, as well: the possibility that it may help illuminate the puzzling aspects of quantum mechanics which show up in the measurement problem, or the nature of quantum chaos [1] [2], or that it may lead to entirely new ideas for interesting physical devices, or new techniques for old problems in precision measurement, the maintenance of coherence, and other fields. This chapter will outline, in fairly nontechnical fashion, the fundamentals of these two key aspects of ....
C. M. Caves and R. Schack, "Unpredictability, information, and chaos," Complexity, vol. 3, no. 1, pp. 46--57, 1997.
Hypersensitivity and Measurements in the Quantum Kicked Top - Breslin, Milburn (Correct)
....decreases. As required by Landauer s principle [20,18] information and entropy must be considered equivalent in thermodynamic terms [15] so the entropy reduction can never exceed the information increase, DeltaI (OE) DeltaH ( 2 ) Gamma DeltaH (OE) 29) if the Second Law is to be obeyed [21]. With these definitions and constraints, Schack et al. define a system that is hypersensitive to perturbation as one for which DeltaI (OE) AE DeltaH ( 2 ) Gamma DeltaH (OE) 30) That is, the amount of information required to describe a system with finer resolution is much greater than ....
C.M. Caves and R. Schack, "Unpredictability, information , and chaos", unpublished.
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